(6)

Step 1:

(a)

Find .

The function is .

As tends to , become arbitrarily large.

Hence, approaches to positive large number.

As tends to , approaches to positive large number.

.

Step 2:

(b)

Find .

The function is .

As tends to , become arbitrarily large.

Hence, approaches to positive large number.

As tends to , approaches to positive large number.

.

Solution :

(a) .

(b) .

(7_a)

Find .

The function is .

As tends to , the first  is zero, second and third terms are large positive in the function.

approaches to negative large number.

As tends to , approaches to negative large number.

.

Solution :

.

(7_b)

Find .

The function is .

As tends to , the first  is large positive number, second and third terms are approximately equal to 0 in the function.

approaches to positive large number.

As tends to , approaches to positive large number.

.

Solution :

.

(8)

Evaluate .

As tends to , become arbitrarily large.

approaches to large positive number.

As tends to , approaches to large positive number.

Solution: